One of my colleagues was asked the following brain teaser or puzzle during an interview at Goldman Sachs & Co.:

You have two identical breakable objects, such as glass pebbles. You are standing in front of a 100-story building and you are told that staring at certain floor, the objects start breaking as you drop them off the balcony. What is the optimal (i.e. minimum number of tries) solution to find out which floor the objects start breaking at?

For example, you can take the approach of binary search. Drop the object down from the 50th floor. If it breaks, you will have to start from the second floor and if the floor you are looking for is truly the 50th, you will have to try 48 more times, totaling in 49 tries. If the object didn’t break, you can try the 75th floor, etc. This, however, is not the optimal solution.

I asked my friend, Radu Gabudean, to solve the question. He told me that I had asked him the same question a year ago and that he had already told me the solution. I challenged him by saying that I wasn’t sure what he was talking about and if he wanted me to take him seriously at all, he should prove it. Two hours later, he sent me the solution and the proof. Don’t mess with the finance PhDs!

Paul Erdös was on of the most influential and greatest mathematicians of the 20th century. Erdös Number describes the collaborative distance from the great mathematician.

I have co-authored two papers while at Stanford: Efficient Web Form Entry on PDAs and Efficient Web Browsing on Handheld Devices Using Page and Form Summarization, so I was wondering if I too had an Erdös Number. If you have ever published a paper in a journal, you can try to find out your Erdös Number by first visiting the Erdös Number Project website.

After little research, I found out that Paul Erdös co-authored a paper with Ronald Graham, who co-authored a paper with Jeffrey Ullman, who, in turn, has co-authored a book and several papers with Hector Garcia-Molina, who co-authored the two papers with me. Thus, the “collaborative distance” from Erdös is 4.

I then looked at some of the other individuals that have Erdös Number 4 and I found names like Bill Gates, Stephen Hawking, Linus Pauling, and Karl Popper. Not a bad company.

I have to give most of the credit for being able to do the research to Orkut Büyükkökten whose research the papers were based on. Orkut was a great mentor and during the years that we worked together, I got introduced to a lot of interesting and great minds.

I found this quite amusing… I mean: I funod tihs qiute aumisng! I discovered this quote on someone else’s blog.

i cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdanieg. The phaonmneal pweor of the hmuan mnid, aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it dseno’t mtaetr in waht oerdr the ltteres in a wrod are, the olny iproamtnt tihng is taht the frsit and lsat ltteer be in the rghit pclae. The rset can be a taotl mses and you can sitll raed it whotuit a pboerlm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Azanmig huh? yaeh and I awlyas tghuhot slpeling was ipmorantt!